The Gemara states that one of the days that the Kohanim Duchened during Minchah was the day upon which a Ma'amad davened in their city. Rashi explains that there is no concern on a fast day for drunkenness, and this why the Kohanim duchaned on the day of a Ma'amad, when the members of a Ma'amad fasted.
The Kohanim in the city, however, were obviously not part of the Ma'amad, or even the current Mishmar, as they were not in the Beis ha'Mikdash. Given this, they were not fasting. How, then, were they able to Duchen?
Moshie Cohen, Yerushalayim
(a) Are there Kohanim in the Ma'amad, Davening that Hash-m should accept our Korbanos just like the Yisrae'lim? Rashi learns that Kohanim were also part of the Ma'amad in Yerushalayim, as the Mishnah (Ta'anis 26a) implies (see Rashi Ta'anis 15b DH Anshei Ma'amad). The Tehilah l'Yonah cites proof for Rashi's assertment from our Sugya; those were the Kohanim who would fast and Duchan with the M'amad.
However, the Ritva (Ta'anis 26a) and Rambam learn that only Yisra'elim took part in the Ma'amad; the Kohanim took part in the Mishmar but not in the Ma'amad. According to them, your question remains; which Kohanim were permitted to Duchan?
It is true that the Kohanim who served in the Mikdash were not allowed to drink wine, so they certainly should be allowed to Duchan. However, the Mishnah implies that it is permitted for the Kohanim to Duchan because of the Ta'anis, the fasting, and not because they are not drinking wine for another reason.
(b) You are assuming that if a Kohen is part of the Ma'amad, it means that it is his Mishmar and he must be in Yerushalayim serving in the Mikdash. However, not every Kohen is able-bodied enough to travel to Yerushalayim and perform the Avodah. In addition, Ba'alei Mumim may not have come to Yerushalayim since they could not perform Avodah in the Mikdash. These Kohanim remained in their city. Perhaps they would join the Yisraelim of the city in their Ma'amad, and they would fast along with them.
(c) There was fasting during the Ma'amad only Monday through Thursday. What about Duchaning? The Ritva and Me'iri on the Mishnah (Ta'anis 26a) say that Duchaning was also only performed Monday through Thursday. However, the Rambam (Klei ha'Mikdash 6:4) learns that it was every day, even when not fasting!
The Rashash (Ta'anis 26b on Rashi DH Ha'idna) suggests that since these are days of prayer and beseeching, the possibility of drinking is quite remote. This might answer your question as well, since even if the Kohanim in the city were not part of the Ma'amad they would still be affected by the strong aura of prayer in the city.
(c) The Tehilah l'Yonah mentions another solution. Can a Kohen who eats on a public fast day, for whatever reason, Duchan? The Pri Chadash (129) says no. However, the Ginas Veradim (Orach Chaim 1:49) says yes. If so, the Kohanim that eat could Duchan during Ma'amados, since it was a fast day for others.
(This may not be an appropriate comparison, however, since the Kohanim were never part of the fast of the Ma'amad in the first place.)
All the best,
Reuven Weiner and M. Kornfeld